Exploring Theoretical Limits of Known Operator Learning and Applications in Motion Compensated Reconstruction

• Applicant: Professor Dr.-Ing. Andreas Maier
• Subject Area: Medical Informatics and Medical Bioinformatics ; Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Medical Physics, Biomedical Technology
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 565055367

In this project, we explore the concept of Known Operator Learning, i.e. the integration of prior knowledge, into machine learning approaches. Such prior knowledge has been shown to reduce the maximal training error bounds. The proof was demonstrated to apply to feed-forward networks of arbitrary depth. Of particular interest to known operator Learning are physical processes that provide knowledge in mathematical terms. Functions or operations with analytical derivatives can be integrated into neural networks, straight-forwardly. Many physical problems are described in terms of partial differential equations and inversion techniques are used to reconstruct a starting point from physical measurements obtained by experiment. One domain in which known operators became increasingly popular is medical image reconstruction. On the one hand, known operators allow the use of physical knowledge which reduces the number of free parameters and therewith the amount of required training data. On the other hand, medical imaging is a domain that requires high safety standards for which known operators are well suited with respect to training error reduction and interpretability. As such medical inverse problems seem to be an ideal choice for the application of known operator learning. Yet, inverse problems such as medical image reconstruction are often solved using iterative approaches which are currently not covered by known operator theory. Hence, the theoretical investigation thereof seems promising to understand fundamental limitations and requirements of such deep learning reconstruction approaches. Furthermore, real-world clinical systems such as C-arm systems hold a plethora of clinical challenges such as patient motion which are not yet compatible with the known operator framework of learning. Development of such theory and applications will enhance clarity regarding the clinical safety of these approaches which might hold as similar relevance for patient safety as radiation dose verification.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Adam Wang, Ph.D.